Based on our previous results showing that triaxial saddles are abundant in SH nuclei [1]}, we consider that quadrupole
triaxial shapes have to be necessarily included.
We treated the effects of mass-asymmetry and nonaxial higher multipoles
as corrections and analysed them at the second stage of calculations.
A rationale for a lesser importance of mass-asymmetric saddles is that,
while they constitute a second, more deformed (\(\beta _{20}\approx 0.7 - 0.8)\) ,
prominent barrier peak in actinides, their heights are much reduced
in SH nuclei where they become irrelevant. In the remaining, less deformed
saddles the mass asymmetry occurs less frequently.
As to the nonaxial multipoles of higher order, they are less important
for saddles with small to moderate \(\gamma \)  [where \(\gamma \)  is the
Bohr's quadrupole nonaxiality parameter, cf. Eq. (REF )].
They become important for \(\gamma \)  closer to 60o
where they are needed to produce oblate shapes having \(x\)  as the symmetry
axis.
Thus, they should be included for nuclei with a large
oblate g.s. deformation and a short triaxial barrier.
The additional studies of the mass-asymmetry and higher nonaxial multipoles
are described in the proper subsections of the Results section.
